Asymptotic behavior for the Vlasov-Poisson equations with strong external magnetic field. Straight magnetic field lines

International audienceThe subject matter of this paper concerns the Vlasov-Poisson equations in the framework of magnetic confinement. We study the behavior of the Vlasov-Poisson system with strong external magnetic field, when neglecting the curvature of the magnetic lines. The arguments rely on averaging techniques. We intend to determine second order approximations and to retrieve the usual electric cross field drift, the magnetic gradient drift, etc